Remote magnetometry using Zeeman spectroscopy

(Zeeman atomic absorption spectroscopy)

## The Zeeman effect

The Zeeman effect is the splitting of energy levels of atoms and molecules upon the presence of a magnetic field (Figure 1). The effect describes the splitting of spectral lines by a magnetic field into multiple closely spaced lines, with the spacing of the lines being dependent on the strength of the magnetic field. Due to this, the spacing can be used to measure the magnetic field of distant bodies such as the Sun and other stars, the Earth and also plasmas.

The dependence of the sublevel energies to the magnetic field is described by the Breit-Rabi formula:

https://en.wikipedia.org/wiki/Zeeman_effect#/media/File:Breit-rabi-Zeeman.png

http://demonstrations.wolfram.com/BreitRabiDiagram/

An example demonstrating how to calculate the solar magnetid field from spectroscopic data is provided at this reference.

Figure 1: In a low magnetic field, we observe one spectroscopic line corresponding to a transition from 3s to 3p. In a medium strength magnetic field, the 3p energy level is split into two sublevels and as a result we observe two transitions and two spectroscopic lines. In a high strength magnetic field, the spacing of the lines is increased. By analysing the spacing, we can determine the magnetic field strength (reproduction based on this reference).

## Zeeman effect demonstration

How we can measure the magnetic field by taking a sample of light!

Video demonstration by the European Southern Observatory (ESO)
Featured in Wikipedia article on the Zeeman effect

Figure 2: Demonstration of the Zeeman effect: composite figure created from captures of ESO video https://youtu.be/SRTP-Obia0w.
Description: Initially (left panel), there is one spectral line and as the strength of the magnetic field increases it splits in three components. With further magnetic field strength increase, the distance between the three spectral lines becomes greater.

Video demonstration by Synctrotron SOLEIL

20-second demonstration of the Zeeman effect starting at t=120 of video by Synctrotron SOLEIL https://youtu.be/tcpBwgN5hlE?t=120

"By approaching a magnet to the sodium lamp, the characteristic yellow line of sodium is subdivided, proving that the electron experiences an electromagnetic force that modifies its energy levels."

Transcript translation (starting at t=54 https://youtu.be/tcpBwgN5hlE?t=54):

(In 1913) "Bohr's atomic model was describing correctly the hydrogen atom. The electron was rotating in circular orbits corresponding to authorized energy levels. By describing the orbits with positive integers, 1, 2, 3 etc. Niels Bohr was introducing the first quantum number of modern physics. As his model was struggling to describe multi-electron atoms, the German physicist Arnold Sommerfeld improved it in 1916 by providing electrons with two additional degrees of freedom: being able to rotate on elliptical orbits like the planets of the solar system as well as modify their trajectory in the presence of a magnetic field. Sommerfeld was thus adding two numbers: "l" the "orbital quantum number" and "m" the "magnetic quantum number". "

"Magnetic because the electrons behave like a small electrical circuit that is sensitive to external magnetic fields. This is the Zeeman effect, named after the Dutch physicist that discovered it twenty years ago when he studied the sodium spectrum. By approaching a magnet to the sodium lamp, the characteristic yellow line of sodium, is subdivided, proving that the electron experiences an electromagnetic force that modifies its energy levels."

Figure 3: Demonstration of the Zeeman effect: by approaching a magnet to the sodium lamp, the characteristic spectroscopic yellow line of sodium is split in three lines (video by Synctrotron SOLEIL https://youtu.be/tcpBwgN5hlE).

## Magnetography based on the Zeeman effect

Magnetograms can be compared to pictures representing magnetic data (Figure 4). They are generated by magnetographs which are telescope instruments that measure the magnetic field of distant bodies like the Sun by analysing emissions from molecules and atoms for Zeeman splitting of spectroscopic lines which are magnetically sensitive. Emitted photons also have a polarization depending on the transition they resulted from and it is quite common to analyse polarization data for magnetic field strength determination. A typical filter based magnetograph consists of a polarimeter, a narrow-band spectrometer (filter) and an imager (CCD camera).

One of the largest of these telescopes was the Mount Wilson Observatory (MWO) 150-foot solar tower built in 1912 (ref.), which was equipped with next generation magnetographs in 1957 (ref.) and had taken daily magnetographs until 2013 (it was last managed by UCLA).  Spectroscopic lines that were examined by this magnetograph included (ref.): Ca II K line at 3933.7Å, Cr II at 5237.325Å, Fe I line at 5250.2Å, Na I D1 at 5895.9Å, Na D2 at 5890.0Å, Ni I at 6767.8Å and Ni I at 6767.782Å.

The NASA-Marshall Space Flight Center (Alabama) Vector Magnetograph Facility was assembled in 1973 to support the Skylab mission. Daily magnetograms can be accessed since 2000 (ref.). The solar vector magnetograph (picture) examines the Fe I line at 5250.2 Å which is influenced by the Zeeman effect and which corresponds to a transition having a specific polarization profile.

The Wilcox Solar Observatory magnetograph at the Stanford campus has been generating daily magnetograms since 1976.

The NASA Solar Dynamics Observatory (SDO) satellite carries the HMI instrument which examines the 6173 Å line and produces daily magnetograms (available at the HMI site and on the SDO site under "colorized magnetogram", Figure 4) .

Figure 4: Magnetogram (colorized) of the Sun on 2018-08-15 generated by the HMI instrument of the NASA SDO satellite (from this link).

## Remote magnetometry of the Earth's magnetic field using the oxygen line and radiometers from the ground or satellites

The Earth’s magnetic field interacts with the oxygen dipole and causes a splitting of O2 energy states (Figure 5). An indicative ground measurement represented by the study of Navas-Guzmán et al 2015 uses the 53.07 GHz emission of oxygen (in the stratosphere) which consists of an emission of polarized photons (polarized emission) in the microwave spectrum. The authors use a radiometer for 51–57 GHz with a digital FFT spectrometer. Additional references can be found at the dissertation of one of the authors (Larsson R 2016).

Representative satellite studies cited by the above study are the following:

1) The 61 GHz radiometer of the Millimeter-wave Atmospheric Sounder (MAS) on the NASA space shuttle of the ATLAS mission measured the 61 GHz oxygen emission (Hartmann G. K. et al 1996).

2) The Special Sensor Microwave Imager/Sounder (SSMIS) on board the U.S. Air Force Defense Meteorology Satellite Program F-16 satellite measured different oxygen magnetic dipole transitions (Han Y et al 2010) which were used to inform two models (cf. weather prediction).

Figure 5: Oxygen transitions (images from presentation related to a NASA mission).